Out of a circular piece of paper, you wish to form a cone cup, so you cut out a circle wedge (with its extreme at the circle center) and join the resulting straight sides, forming a conical cup.

What size should the wedge be, to maximize the capacity of the cone?

How about an extension to this problem so that the wedge removed is also made into a second cup.  What angle is needed to maximise the volume of the two cups combined.

I thought this might be an interesting part B to the problem but I got scared by the equation I formed trying to solve it.  Can anyone help?

Posted by Alec on 2005-04-09 10:09:56